Recently, 12442 system of Fe-based superconductors has attracted considerable attention owing to its unique double-FeAs-layer structure. A steep increase in the in-plane upper critical field with cooling has been observed near the superconducting transition temperature, $T_c$, in KCa$_2$Fe$_4$As$_4$F$_2$ single crystals. Herein, we report a high-field investigation on upper critical field of this material over a wide temperature range, and both out-of-plane ($H|c$, $H_{c2}^{c}$) and in-plane ($H|ab$, $H_{c2}^{ab}$) directions have been measured. A sublinear temperature-dependent behavior is observed for the out-of-plane $H_{c2}^{c}$, whereas strong convex curvature with cooling is observed for the in-plane $H_{c2}^{ab}$. Such behaviors could not be described by the conventional Werthamer--Helfand--Hohenberg (WHH) model. The data analysis based on the WHH model by considering the spin aspects reveals a large Maki parameter $alpha=9$, indicating that the in-plane upper critical field is affected by a very strong Pauli paramagnetic effect.
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